Xiong Jin

Page contents:

• Research interests
• Teaching
• Publications

Research interests

Multiplicative chaos theory and related topics: probability theory, geometric measure theory, ergodic theory, quasiconformal mappings and Quantum gravity, spectral theory.

Teaching

• 2018/2019 Semester 2: Brownian Motion/Stochastic Modeling in Finance
  
• 2017/2018 Semester 2: Random Models/Stochastic Modeling in Finance
  
• 2016/2017 Semester 2: Random Models/Stochastic Modeling in Finance
  
• 2015/2016 Semester 2: Random Models/Stochastic Modeling in Finance
  

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Publications

• X. Jin: Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion, arXiv:1705.01726, (2017). (arXiv)
• K. Falconer and X. Jin: Exact dimensionality and projection properties of Gaussian multiplicative chaos measures, Trans. Amer. Math. Soc., to appear (2018). (arXiv)
• C. Bruce and X. Jin: Projections of Gibbs measures on self-conformal sets, Nonlinearity, to appear (2018). (arXiv)
• K. Falconer and X. Jin: Self-Similar Sets: Projections, Sections and Percolation, In: Trends in Mathematics, Recent Developments in Fractals and Related Fields, J. Barral, S. Seuret ed., Birkhaeuser, Switzerland, 113-127 (2016). (pdf)
• K. Falconer, J. Fraser and X. Jin: Sixty Years of Fractal Projections, In: Progress in Probability 70, C. Bandt; K. Falconer; M. Zaehle ed., Birkhaeuser, Switzerland, (2015). (arXiv)
• K. Falconer and X. Jin: Dimension conservation for self-similar sets and fractal percolation, Int Math Res Notices 2015(24), 13260–13289 (2015). (arXiv)
• K. Falconer and X. Jin: Exact dimensionality and projections of random self-similar measures and sets, J. London Math. Soc. 90(2), 388-412 (2014). (arXiv)
• J. Barral and X. Jin: On exact scaling log-infinitely divisible cascades, Probab. Theory Relat. Fields. 160, 521--565 (2014). (pdf)
• X. Jin: A unifrom dimension result for two-dimensional fractional multiplicative processes, Ann. Inst. Henri Poincare Probab. Stat. 50(2), 512--523 (2014). (pdf)
• J. Barral, X. Jin, R. Rhodes and V. Vargas: Gaussian multiplicative chaos and KPZ duality, Comm. Math. Phys. 323(2), 451--485 (2013). (pdf)
• X. Jin: Dimension result and KPZ formula for two dimensional multiplicative cascade processes, Ann. Probab. 40(1), 1--18 (2012). (arXiv)
• X. Jin: The graph and range singularity spectra of b-adic independent cascade functions, Adv. Math. 226, 4987--5017 (2011). (pdf)
• X. Jin: The graph and range singularity spectra of random wavelet series built from Gibbs measures, Nonlinearity 23, 1449--1475 (2010). (arXiv)
• J. Barral and X. Jin: Multifractal analysis of complex random cascades, Comm. Math. Phys. 297, 129--169 (2010). (pdf)
• J. Barral, X. Jin and B. Mandelbrot: Convergence of complex random cascades, Ann. Appl. Probab. 20(4), 1219--1252 (2010). (arXiv)
  
• J. Barral, X. Jin and B. Mandelbrot: Uniform convergence for complex [0,1]-martingales, Ann. Appl. Probab. 20(4), 1205-1218 (2010). (arXiv)
  

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